Getting the Job Done—Speed 06:16 minutes

Video Transcript

Transcript Getting the Job Done—Speed

Patagonian power couple Tatu and Princess finally have some time off from their busy work schedule to spend the day together. But going on a date is not always so easy, in the wilds of the South American desert. Interrupting their idyllic morning, it's that jerk vulture, Walter. Why's he always ruining people's dates? If Tatu is going to save Princess and what's left of their quiet day off, he's going to have to get the job done with speed! It looks like Walter has kidnapped Princess and taken her back to his nest. So how far does Tatu have to go to catch him? To find this out, we can use a formula which you may remember... Distance is equal to rate times time. This common formula can be shortened to 'd' equals 'r' times 't'. If we know that Walter flies at a rate of 80 feet per second and it will take him 3 seconds to reach his nest, we can use this information to solve for the distance, 'd'. We already know the rate is 80 feet per second, so we can plug that in for 'r,' and we know the time is 3 seconds, so we can plug that in for 't'. Now to solve for 'd', just simplify, starting with the units. Just as you can cancel-out common factors, like-units cancel out as well. For example, here, we can cancel out the seconds unit because it is in both the numerator and denominator. Now we just multiply 80 feet by 3, to get 240 feet. That's pretty far for an armadillo, so Tatu had better hurry if he's going to rescue Princess! Oh no! It's even worse than usual! Walter’s annoying Princess with his boring old photo album! How long will she have to suffer before Tatu can rescue her? Let's start with what we know. In the last example, we found out that the distance to the nest is 240 feet. If we also know that Tatu can move at a rate of 40 feet per second, we can use the same formula of distance equals rate times time and solve for the unknown variable, 't'. To do that, let's rewrite the equation by dividng both sides by 'r'.
Now that we have isolated 't', we can substitute 240 feet in for the distance, 'd,' and 40 feet per second for the rate, 'r'. We can rewrite the left side of the equation by changing division to multiplication. Notice how we flipped our numerator and denominator, since dividing by a fraction is the same as multiplying by its reciprocal. Just as we did before, the feet units cancel out. Which leaves us with 240 seconds divided by 40. So time is equal to 6 seconds. We can tell that we correctly canceled our units, because we were solving for time and we are left with 'seconds'. With Princess safe from the clutches of extreme boredom, this endangered couple are going to have to make tracks and find somewhere Walter can’t bother them. What about that coffee shop? The sign says it's one mile away and there are no birds allowed! So how fast are they going to have to run to beat Walter there? Let's look at the information we already have. The coffee shop is one mile away, so that's our distance. And let's say they have 2 minutes to get there. We are solving for rate and we're going to want that in feet per second. Hmm...hold on... miles, minutes, feet, seconds? Before we can calculate the rate, we need to convert to the same units. We know that 1 mile is equal to 5,280 feet, and 2 minutes equals 120 seconds. And that's it: now we can solve our problem in feet per second. To do this, let's use distance equals rate times time, but for this example, solve for the rate. To set up our equation, let's isolate 'r' by dividing both sides by 't'. This simplifies to 'd' over 't' equals the rate 'r'. Now we can substitute 5,280 feet for the distance 'd' and 120 seconds for the time 't'. After simplifying, we are left with a rate of 44 feet per second. To review... Using the formula distance equals rate times time, we can calculate distance or rewrite the equation and solve for time or solve for rate. Once you have isolated the variable you want to solve for, simply substitute the known values and simplify, starting with the units. If the units don't cancel, you might have to use what you know about converting to other units. Whoa, at that rate, those guys are definitely going to beat Walter to the coffee shop but, oh no, it looks like they're closed for the holidays. I guess Tatu and Princess are going to have to spend their date with Walter and his photo album ...wont wont...